Problem: Multiply the following complex numbers: $({-1-i}) \cdot ({5-3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-i}) \cdot ({5-3i}) = $ $ ({-1} \cdot {5}) + ({-1} \cdot {-3}i) + ({-1}i \cdot {5}) + ({-1}i \cdot {-3}i) $ Then simplify the terms: $ (-5) + (3i) + (-5i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -5 + (3 - 5)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -5 + (3 - 5)i - 3 $ The result is simplified: $ (-5 - 3) + (-2i) = -8-2i $